57332012engpreprint12012-04-25----Matrix methods for computing Eigenvalues of Sturm-Liouville problems of order fourThis paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's method as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods are investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated.urn:nbn:de:kobv:517-opus-592795927RVK-Klassifikation: SI 990Keine Nutzungslizenz vergeben - es gilt das deutsche UrheberrechtAmornrat RattanaChristine BöckmannPreprints des Instituts für Mathematik der Universität Potsdam1(2012)13enguncontrolledFinite difference methodenguncontrolledNumerov's methodenguncontrolledBoundary value methodsenguncontrolledFourth order Sturm-Liouville problemenguncontrolledEigenvaluesMathematikBoundary eigenvalue problemsSturm-Liouville theory [See also 34Lxx]Numerical approximation of eigenvalues and of other parts of the spectrumEigenvalue problemsopen_access2012Institut für MathematikUniversität Potsdamhttps://publishup.uni-potsdam.de/files/5733/premath13.pdf3479720132013eng144156138249articleElsevierAmsterdam1------Matrix methods for computing eigenvalues of Sturm-Liouville problems of order fourThis paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions. Furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's methods as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods is investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated.Journal of computational and applied mathematics10.1016/j.cam.2013.02.0240377-0427 (print)1879-1778 (online)wos:2011-2013WOS:000318133500013Rattana, A (reprint author), Univ Potsdam, Inst Math, Neuen Palais 10, D-14469 Potsdam, Germany., karattana@hotmail.com; bockmann@rz.uni-potsdam.deAmornrat RattanaChristine BöckmannenguncontrolledFinite difference methodenguncontrolledNumerov's methodenguncontrolledBoundary value methodsenguncontrolledFourth order Sturm-Liouville problemenguncontrolledEigenvaluesInstitut für MathematikReferiert3405420132013eng121 S.doctoralthesisPotsdam1------Direct and inverse sturm-liouville problems of order fourallegro:1991-201410111176Potsdam, Univ., Diss., 2013Amornrat RattanaInstitut für Mathematik